The Stanley’s Conjecture on Cohen-Macaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, Soleyman-Jahan and Yassemi. As a consequence of our results Stanley’s Conjecture holds in 5 variables.

Let p(n) denote the number of unrestricted partitions of n. For i = 0, 2, let pi(n) denote the number of partitions π of n such that O(π)−O(π) ≡ i (mod 4). Here O(π) denotes the number of odd parts of the partition π and π is the conjugate of π. R. Stanley [13], [14] derived an infinite product representation for the generating function of p0(n)− p2(n). Recently, H. Swisher [15] employed the ci...

T issue of the Journal of Physical Chemistry B is dedicated to H. Eugene (Gene) Stanley, William Fairfield Warren Distinguished Professor and Professor of Physics, Chemistry, Biomedical Engineering, and Physiology at Boston University. The scope of Gene Stanley’s research accomplishments is virtually unparalleled in the physical sciences. In more than 1000 publications, he has made groundbreaki...

At the MONICA conference “MONomial Ideals, Computations and Applications” at the CIEM, Castro Urdiales (Cantabria, Spain) in July 2011, I gave three lectures covering different topics of Combinatorial Commutative Algebra: (1) A survey on Stanley decompositions. (2) Generalized Hibi rings and Hibi ideals. (3) Ideals generated by two-minors with applications to Algebraic Statistics. In this artic...